Gilchrist, 28, is a former second-round pick of the Chargers back in 2011. After four years San Diego, Gilchrist signed a four-year, $22 million contract with $8.5 million guaranteed in March of last year.
Gilchrist stands to make base salaries of $5 million and $6 million over the next two years.
In 2016, Gilchrist appeared in 13 games and recorded 55 tackles, two interceptions, a forced fumble and three pass defenses.
Giacomini, 31, is a former fifth-round pick of the Packers back in 2008. He spent four years with the Seahawks before signing a four-year, $18 million contract that includes $7 million guaranteed with the Jets.
Giacomini stands to make base salaries of $4.5 million over the next two years.
In 2016, Giacomini appeared in five games for the Jets and is rated by Pro Football Focus as the No. 62 offensive tackle out of 78 qualifying players.